12x^2-76x-40=

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Solution for 12x^2-76x-40= equation:


Simplifying
12x2 + -76x + -40 = 0

Reorder the terms:
-40 + -76x + 12x2 = 0

Solving
-40 + -76x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + -19x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-10 + -19x + 3x2)' equal to zero and attempt to solve:

Simplifying
-10 + -19x + 3x2 = 0

Solving
-10 + -19x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-3.333333333 + -6.333333333x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + -6.333333333x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + -6.333333333x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + -6.333333333x + x2 = 0 + 3.333333333
-6.333333333x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
-6.333333333x + x2 = 3.333333333

The x term is -6.333333333x.  Take half its coefficient (-3.166666667).
Square it (10.02777778) and add it to both sides.

Add '10.02777778' to each side of the equation.
-6.333333333x + 10.02777778 + x2 = 3.333333333 + 10.02777778

Reorder the terms:
10.02777778 + -6.333333333x + x2 = 3.333333333 + 10.02777778

Combine like terms: 3.333333333 + 10.02777778 = 13.361111113
10.02777778 + -6.333333333x + x2 = 13.361111113

Factor a perfect square on the left side:
(x + -3.166666667)(x + -3.166666667) = 13.361111113

Calculate the square root of the right side: 3.655285367

Break this problem into two subproblems by setting 
(x + -3.166666667) equal to 3.655285367 and -3.655285367.


Subproblem 1
x + -3.166666667 = 3.655285367

Simplifying
x + -3.166666667 = 3.655285367

Reorder the terms:
-3.166666667 + x = 3.655285367

Solving
-3.166666667 + x = 3.655285367

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3.166666667' to each side of the equation.
-3.166666667 + 3.166666667 + x = 3.655285367 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + x = 3.655285367 + 3.166666667
x = 3.655285367 + 3.166666667

Combine like terms: 3.655285367 + 3.166666667 = 6.821952034
x = 6.821952034

Simplifying
x = 6.821952034


Subproblem 2
x + -3.166666667 = -3.655285367

Simplifying
x + -3.166666667 = -3.655285367

Reorder the terms:
-3.166666667 + x = -3.655285367

Solving
-3.166666667 + x = -3.655285367

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3.166666667' to each side of the equation.
-3.166666667 + 3.166666667 + x = -3.655285367 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + x = -3.655285367 + 3.166666667
x = -3.655285367 + 3.166666667

Combine like terms: -3.655285367 + 3.166666667 = -0.4886187
x = -0.4886187

Simplifying
x = -0.4886187


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.821952034, -0.4886187}
Solution
x = {6.821952034, -0.4886187}

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